Discrete Programming Method Research Articles

Construction of a cable yarding track by mathematical and software methods

Constraining factors for the development of traditional solutions for the development of hard-to-reach logging areas are given. Mathematical and software methods are proposed to calculate the construction of routes for rope-trailer installations. Methods of solving the problem of laying an acceptable optimal route using discrete programming methods under conditions of risk and uncertainty are proposed. On a practical example in typical natural and industrial conditions of the North-West Federal District of the Russian Federation (sq.4 v.39 of the Primorsky district forestry of the Kurortny forestry of St. Petersburg) the construction of a mathematical model for solving the stochastic problem with quantile indices is carried out.

Optimization of the task of forming a management system of hierarchical multilevel complex organizational systems

A hierarchical configuration procedure in the process of analyzing the functioning of organizational structures using algorithms for solving problems using discrete programming methods is considered in detail in this paper. On the basis of the research, the authors propose a methodology for the combined application of an initial approximation algorithm with certain properties and an algorithm for a recursive procedure for a directed search for the optimal hierarchy, which, in the future, solving the traveling salesman problem in a minimum time much more efficient than using the methods of dynamic programming of branches and boundaries.

Method for optimization of frequency resource allocation with frequency reuse for cognitive radio system

The concept of cognitive radio can be described as a radio with the study of capabilities, i.e. as a radio that is able to gain knowledge about the radio environment and adjust its operating parameters and protocols accordingly.
 The task of minimizing the frequency band is relevant at the stage of the cognitive radio network functioning when distributing the frequency resource between subscriber stations. With the ever-growing demand for frequency bands, this challenge is driven by the need to improve the efficient use of the radio frequency spectrum through frequency reuse methods.
 This paper proposes a method for ensuring the reuse of frequencies based on obtaining estimates of mutual distances between subscriber stations in real time. An algorithm is proposed for solving the problem of frequency resource allocation optimization for a cognitive radio network with frequency reuse. The algorithm is based on the method of local optimization, one of the approximate methods of discrete programming. In this case, the condition of local optimality is that the operating frequency assigned to the next subscriber station must be the closest to the frequency assigned in the previous step.
 The efficiency of the frequency resource optimization algorithm for the LTE network was analyzed using simulation modeling. The dependences of the bandwidth on the number of subscriber stations served are obtained. The analysis showed that the use of this algorithm allows to reduce the frequency band by 2 -3 times. The analysis also showed that the efficiency of the algorithm increases with the growth of the number of subscriber stations served simultaneously.

Statement and Solution of Multicriteria Tasks of Database Modular Block-Schemes Development

The paper considers developed and offered an effective algorithm for solving the block-symmetrical tasks of polynomial computational complexity of data processing modular block-schemes designing. Currently, there are a large number of technologies and tools that allow you to create information systems of any class and purpose. To solve the problems of designing effective information systems, various models and methods are used, in particular, mathematical discrete programming methods. At the same time, it is known that such tasks have exponential computational complexity and can not always be used to solve practical problems. In this regard, there is a need to develop models and methods of the new class, which provide the solution of applied problems of discrete programming, aimed at solving problems of large dimensions. The work has developed and proposed block-symmetric models and methods as a new class of discrete programming problems that allow us to set and solve applied problems from various spheres of human activity. The issues of using the developed models are considered. and methods for computer-aided design of information systems (IS).

Optimal sea floor placement of the oil/gas production equipment

In the construction designing of oil field surface facilities, exists a problem of the seabed production equipment optimal placement. As an initial approximation, we can represent this task in the form of the linear Boolean programming problem. An application of routine methods of discrete programming can theoretically give the desired solution. However, these methods do not take into account the specific nature of the problem. This problem belongs to the NP class. So we can run into significant computational difficulties. This situation is typical for construction of the ground surface or subsea located facilities for real oil/gas fields. To overcome it, we propose to replace a discrete programming model with a linear programming one, which takes into account problem-specific properties. Also, we present examples of the application of the proposed parallel optimization algorithms. Input data for them: the seabed profile, geometry, and space distribution of oil/gas reserves. Optimization problem objective function is the penalty for the irrational placement of seabed production equipment elements.

METHOD FOR DETECTION OF SIGNALS PRIMARY USERS IN COGNITIVE RADIO NETWORKS

Context. With the advent of mobile communication networks, the signal-interference situation became sharply complicated. An increasing number of radio electronic devices for various purposes lead to the formation of the multiple nature of electromagnetic interactions between them. At the same time, the deficit of frequency resources becomes even more important, the problem of electromagnetic compatibility becomes aggravated. The ways of solving this problem can be found using the cognitive distribution of the frequency resource with repeated use of frequencies. Thus, the optimization of the distribution of the frequency resource in cognitive radio networks and the development of an algorithm for the allocation of a frequency resource with the repeated use of frequencies is an actual scientific task. Objective. The aim of the study is to provide electromagnetic compatibility in the cognitive distribution of resources in a mobile communication network.Methods of research are based on the basic principles of radiophysics, telecommunications theory, system analysis, mathematical statistics, probability theory, optimization theory, mathematical and simulation modeling.Results. The situation and the most electromagnetic situation in mobile communication networks are greatly complicated by the fact that various random factors, which are difficult to forecast, are introduced into this environment. Under these conditions, it is not always possible to calculate the electromagnetic situation in advance and solve the problem of electromagnetic compatibility with sufficient accuracy, and often it is simply impossible due to a priori uncertainty. The problem of electromagnetic compatibility for mobile communication networks must be solved at the stage of its operation in real time. An algorithm for solving the problem of optimization of frequency resource allocation for mobile communication networks is proposed. The algorithm is based on the method of local optimization – one of the approximate methods of discrete programming. In this case, the local optimality condition is that the operating frequency that is assigned to the next subscriber station should be close to the frequency assigned at the previous step, but electromagnetic compatibility requirements must be met.Conclusions. For the first time, a method has been developed for ensuring electromagnetic compatibility in the allocation of a frequency resource in a mobile communication network, which consists of an algorithm with repeated use of frequencies. The use of this method makes it possible to reduce the frequency band by 2 to 3 times.

BLOCK-SYMMETRIC MODELS AND METHODS: NEW CLASS OF DISCRETE PROGRAMMING TASKS

A new class of tasks in setting and solving application-oriented tasks is developed and offered in this paper – block-symmetric models and methods of discrete programming. The general setting of block-symmetric tasks is demonstrated. It differs from the known tasks by the block properties, symmetry and existence of different types of variables. The algorithm of iterative imaging of polynomial computing complexity, allowing to solve the application-oriented tasks of high dimensionality, is developed for solving tasks of this class. The clustering task is stated as an example of setting of the application-oriented task of the discrete programming.

Reactive power compensation in distribution networks of mining enterprises

Large electricity consumers – mining companies – along with active power consumed reactive power, creating network flows. The issues of compensation of reactive power and rational placing of the compensating devices are becoming highly relevant in the light of energy saving policies. Compensation is particularly important when optimization of voltage and power consumption in order to reduce active losses and improve power quality. Effective action for reduction of losses in electric networks is installation of devices of reactive power compensation (RPC). In the analysis of methods of calculation of optimal power compensating devices, and location were taken into account the specificity of mining enterprises, namely the separation of electrical networks underground and surface. The objective function formulated on the basis of annual reduced costs and identified system limitation, when considered in the objective function. The analysis of the objective function showed that it separaely and the problem can be solved by methods of discrete programming.

Dynamic models and algorithms of comprehensive scheduling for ground-based facilities communication with navigation spacecrafts

A multiple-model description of interaction between a ground-based control complex GCC and orbital system (OrS) of navigation spacecrafts (NS) is presented. A dynamic interpretation of operations and control processes is implemented. The proposed approach lets use fundamental scientific results of the modern control theory for new applied problems. In particular, a scheduling problem for GCC ground-based technical facilities was reduced to a boundary problem with the help of the local section method. Scheduling problems of the considered class are usually solved via methods of discrete programming, but when the dimensionality is high, the optimal solution is not provided and heuristic algorithms are needed. This paper introduces an original approach, based on models and methods of optimal control theory, to scheduling problems of high dimensionality.

Resource Allocation for OFDMA-Based Cognitive Radio Networks with Application to H.264 Scalable Video Transmission

Resource allocation schemes for orthogonal frequency division multiple access- (OFDMA-) based cognitive radio (CR) networks that impose minimum and maximum rate constraints are considered. To demonstrate the practical application of such systems, we consider the transmission of scalable video sequences. An integer programming (IP) formulation of the problem is presented, which provides the optimal solution when solved using common discrete programming methods. Due to the computational complexity involved in such an approach and its unsuitability for dynamic cognitive radio environments, we propose to use the method of lift-and-project to obtain a stronger formulation for the resource allocation problem such that the integrality gap between the integer program and its linear relaxation is reduced. A simple branching operation is then performed that eliminates any noninteger values at the output of the linear program solvers. Simulation results demonstrate that this simple technique results in solutions very close to the optimum.

Solving the maxcut problem by the global equilibrium search

The authors propose an approach to the solution of the maxcut problem. It is based on the global equilibrium search method, which is currently one of the most efficient discrete programming methods. The efficiency of the proposed algorithm is analyzed.

Dynamic Models of Comprehensive Scheduling for Ground-Based Facilities Communication with Navigation Spacecrafts

A multiple-model description of interaction between a ground-based control complex (GCC) and orbital system (OrS) of navigation spacecrafts (NS) is presented. A dynamic interpretation of operations and control processes is implemented. The proposed approach lets use fundamental scientific results of the modem control theory for new applied problems. In particular, in this case, a scheduling problem for GCC ground-based technical facilities was reduced to a boundary problem with the help of the local section method. Scheduling problems of the considered class are usually solved via methods of discrete programming, but when the dimensionality is high, the optimal solution is not provided and heuristic algorithms are needed. This paper introduces an original approach, based on models and methods of optimal control theory, to scheduling problems of high dimensionality1.

Multi‐objective combinatorial optimization problems: A survey

AbstractIn the last 20 years many multi‐objective linear programming (MOLP) methods with continuous variables have been developed. However, in many real‐world applications discrete variables must be introduced. It is well known that MOLP problems with discrete variables can have special difficulties and so cannot be solved by simply combining discrete programming methods and multi‐objective programming methods.The present paper is intended to review the existing literature on multi‐objective combinatorial optimization (MOCO) problems. Various classical combinatorial problems are examined in a multi‐criteria framework. Some conclusions are drawn and directions for future research are suggested.

Structural synthesis of sandwich beams with outer layers of box-section

It is proved by model measurements that, for sandwich beams constructed from two rectangular tubes and a damping layer glued between them, the following calculation methods can be applied. Static bending and shear stresses as well as deflections of simply supported beams may be calculated by Allen's formulae for sandwich beams with flexurally stiff faces. The first eigenfrequency and the loss factor can be determined by using the diagrams given in reference [1]. For the loss factors Ungar's formula gives a suitable approximation. A minimum cost design procedure is presented for a sandwich beam with constant cross-section. The unknown dimensions of the cross-section are determined which satisfy the design constraints and minimize the material costs. In a numerical example, constraints relating to the maximal dynamic stresses and deflection as well as local buckling of plate elements are considered. In the optimization the backtrack combinatorial discrete programming method is applied. A numerical comparison shows that the material costs of a sandwich beam are lower than those of a homogeneous box one.

Combinatorial Methods of Discrete Programming

Combinatorial Methods of Discrete Programming